Course Objectives:
1.
Know the development of the binomial theorem; solve
problems using binomial coefficients.
2.
Understand and use Pascal's Triangle.
3.
Solve inequalities (linear, nonlinear, absolute
value).
4.
Graph the solutions of inequalities using open,
closed, half-open, and infinite interval notation.
5.
Find the distance between two given points.
6.
Recognize the equation of a circle, find the
coordinates of the center, and determine the radius (and diameter).
7.
Develop the midpoint formula. Use it to find the
midpoint coordinates of a well-defined line segment.
8.
Make an accurate graph of a given equation in x and
y. Use symmetry tests.
9.
Discuss the meaning of variable and the domain of a
variable.
10.
Explain the meaning of function in terms of domain,
range and one-to one relation.
11.
Know the meaning of identity function, constant
function, even function, and odd function.
12.
Given the graph of a function, state the intervals
over which it is increasing, decreasing, and constant.
13.
Graph a given function.
14.
Know how to shift a graph horizontally and
vertically.
15.
Know how to reflect and/or stretch a graph.
16.
Recognize the equation of a linear function.
17.
Know the meaning of, and how to determine, the slope
of a line.
18.
Write the standard form of a given linear equation
in x and y.
19.
Find the equation of a line using the point-slope
and slope intercept forms.
20.
Know how to add, subtract, multiply and divide
functions.
21.
Determine the specified composite function of two
given functions.
22.
Determine the inverse function of a given one-to-one
function.
23.
Determine if a function is one-to-one.
24.
Know the form of an equation of a quadratic
function.
25.
Graph a given quadratic function.
26.
Find the maximum or minimum value of a given
quadratic function.
27.
Sketch the graph, including all intercepts and
linear asymptotes, of a given rational function.
28.
Sketch the graph of a given exponential function.
29.
Become familiar with the natural exponential
function and some applications of this function.
30.
Sketch the graph of a given logarithmic function.
31.
Know and be able to use the major properties of
logarithms.
32.
Become familiar with common and natural logarithms.
Optional:
1.
Express in equation form a stated variation between
two variable expressions.
2.
Understand the intermediate value theorem.
3.
Understand the remainder and factor theorems.
4.
Understand the fundamental theorem of algebra.
5.
Understand the meaning of the division algorithm for
polynomials.
6.
Know the meaning of multiplicity of a zero of a
polynomial.
7.
Know how to determine the number of zeros of a
polynomial.
8.
Use Descartes' rule of signs.
9.
Understand upper and lower bounds for solutions of
equations.
10.
Determine the rational zeros of a given polynomial
function.
11.
Recognize the equation of a conic section and sketch
the graph.
TENTATIVE
HOMEWORK ASSIGNMENTS
(Assume odd numbered problems.)
